Not usually, they're not particularly deep rooting compared to, say, a Eucalyptus.

They will dry out the soil in the vicinity of a hedge but it would have to be a pretty extensive planting to affect the water table.

When we moved in to our house, the garden was surrounded by Leylandii 20 feet tall. It was horrendous and nothing grew. In the winter our back garden go no sun at all. After we took them out we had so many seedlings of different plants coming our that must have been killed off by these horrendous trees. They are so acidic as well. I suggest you plant something more friendly.